Bounds on the minimum distance of additive quantum codes

Bounds on [[38,26]]2

lower bound:4
upper bound:4

Construction

Construction of a [[38,26,4]] quantum code:
[1]:  [[62, 50, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 62 stacked to height 2 with 4 generating polynomials
[2]:  [[38, 26, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 5, 9, 10, 12, 17, 18, 19, 20, 21, 26, 32, 33, 34, 36, 40, 41, 42, 43, 44, 46, 47, 48, 54, 56 }

    stabilizer matrix:

      [1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1]
      [0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1]
      [0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1]
      [0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0]
      [0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0]
      [0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1|1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1|0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0|1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0|1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1|1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0|1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]

last modified: 2006-04-07

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014